Best background for cut outs
Likely in your situation, you would want to render the dice as a foreground layer, the floor with shadow as a separate layer, and then turn on transparency in the render settings. That way you will get transparency where the black is now.

In Photoshop, you can add a background colour layer with a gradient and blend it into the floor layer easily. No need to render something simple like that.

Render Layer Settings

Please note that the blocks are on Layer 1 of the viewport and the Floor is on Layer 2. In the render layer panel, we select Scene Layers 1 and 2, and then assign Layer 1 to Render Layer 1 (named Blocks) and Layer 2 to Render Layer 2 (named Floor). Make sure the Combined pass is enabled for both layers.



Enable Transparency



In the UV Editor, select Render Result, then you'll have the option to switch between the 2 rendered layers. You can save out each layer as a PNG file (RGBA).



Output Blocks PNG (has alpha channel, though not obvious on SE page here)



Output Floor PNG



Bonus Tip
If you were finding you were re-rendering the image a lot, you could enable compositing and add File Output nodes to write the PNG's to disk as part of the render process. I can detail that process if need be.